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A076366 Number of numbers for which the count of nonprimes (i.e., 1 and composites) in their reduced residue set equals n.

%I A076366 #18 Feb 26 2020 03:34:06
%S A076366 10,6,6,4,4,7,3,4,3,7,4,4,0,6,5,1,4,3,7,4,7,2,3,3,2,2,6,5,2,2,0,6,4,3,
%T A076366 5,4,5,3,1,3,3,4,4,6,2,3,1,6,1,6,3,6,1,4,4,4,1,1,3,6,3,2,4,4,1,1,2,4,
%U A076366 6,0,3,4,3,5,4,1,2,8,2,5,6,2,2,5,1,4,2,4,7,2,1,2,6,1,3,5,2,3,5,3
%N A076366 Number of numbers for which the count of nonprimes (i.e., 1 and composites) in their reduced residue set equals n.
%H A076366 Giovanni Resta, <a href="/A076366/b076366.txt">Table of n, a(n) for n = 1..10000</a>
%F A076366 a(n) = Card{x; A048864(x) = n}; a(n)=0 if supposedly no such number exists (see A072023).
%e A076366 A048864(x) = 13: S = {},                                a(13) =  0;
%e A076366 A048864(x) = 16: S = {144},                             a(16) =  1;
%e A076366 A048864(x) = 22: S = {57,92},                           a(22) =  2;
%e A076366 A048864(x) = 7:  S = {13,34,50},                        a(7)  =  3;
%e A076366 A048864(x) = 4:  S = {15,22,54,84},                     a(4)  =  4;
%e A076366 A048864(x) = 15: S = {35,64,68,156,240},                a(15) =  5;
%e A076366 A048864(x) = 2:  S = {5,10,14,20,42,60},                a(2)  =  6;
%e A076366 A048864(x) = 6:  S = {11,21,32,40,72,78,210},           a(6)  =  7;
%e A076366 A048864(x) = 78: S = {133,177,268,440,490,552,870,990}, a(78) =  8;
%e A076366 A048864(x) = 1:  S = {1,2,3,4,6,8,12,18,24,30},         a(1)  = 10; See A048597.
%o A076366 (PARI) listn(nn) = {my(v = vector(10^5, n, eulerphi(n) - (primepi(n) - omega(n)))); vector(nn, k, if (#(w=Vec(select(x->(x==k), v, 1))) == 0, 0, #w));} \\ _Michel Marcus_, Feb 23 2020
%Y A076366 Cf. A000010, A000720, A001221, A048597, A048864, A048865, A070971, A072022, A072023, A074915.
%K A076366 nonn
%O A076366 1,1
%A A076366 _Labos Elemer_, Oct 10 2002